Inferring a vector wrt a maximization objective!

abhishek2301

Hello,

I have a dataset of 5-dimensional real-valued vector X^j={x_i: i=1,2,3,4,5} and their corresponding y^j where y^j is a real-valued number and j is the no of samples.
Suppose the X^j vectors are various audio feature vectors and the y^j are corresponding user ratings. Now there will be some (non)linear relationship between X^j and y^j where y^j will denote some degree of importance(quality) of the corresponding vector X^j. Then, I want to derive a X^j vector wherein the user rating values or y^j (quality) is maximized (the most likely to be maximized following the relationship distribution between X^j and y^j).
If I take a weighted average of X^j then the result will be converging towards the mean but how can I make it to converge towards the maximum using some sophisticated statistical technique?

Any hint/help is highly appreciated.
Thanks.

viraltux

Hi Abhishek, first of all you don't know if there is only one maximum, in fact, I bet there are potentially many in your problem since not everyone is going to have the same taste for the audios; lovers of classical music will rate differently than lovers of heavy metal and the vectors describing both audios are probably quite different.

Anyway, let's assume for a moment that is not so, one thing you can do is filter your data and keep only high rated vectors and work with them, now you could try to calculate the average but that vector is going to give you a very basic and rough idea of what is going on in your data, specially if your vector's parameters are highly correlated.

I think the best you can do is to analyze your data with a biplot, check this: http://en.wikipedia.org/wiki/Biplot

This kind of plot will give you great insights of what your users are looking for and therefore what kind of vector you need for your purposes.

Good Luck!